The Class of Distributions of Periodic Ornstein–Uhlenbeck Processes Driven by Lévy Processes
✍ Scribed by Jan Pedersen; Ken-Iti Sato
- Publisher
- Springer US
- Year
- 2005
- Tongue
- English
- Weight
- 264 KB
- Volume
- 18
- Category
- Article
- ISSN
- 0894-9840
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## Abstract The infinite (in both directions) sequence of the distributions μ^(__k__)^ of the stochastic integrals \documentclass{article}\usepackage{amssymb}\begin{document}\pagestyle{empty}$\int \_0^{\infty -} c^{-N\_{t-}^{(k)}} dL\_t^{(k)}$\end{document} for integers __k__ is investigated. Here
Let X (N'd) be a N-parameter Omstein-Uhlenbeck process taking values in ~a. In this paper, we prove that, for an arbitrary pair of positive integers (N, d) and any open set S in R d, X (u'd) is recurrent to S. This is surprisingly different from the recurrence properties of the N-parameter Wiener pr